Revisiting Principal-Axes Aligned conies: A unified algebraic constraint and geometric interpretation for camera calibration

In this paper, we present a novel viewpoint of treating conks-based calibration as the algebraic and geometric constraints. From this viewpoint, we use four intersection points correspondence to conduct a unified algebraic constraint of Principal-Axes Aligned (PAA) conies which is a necessary and sufficient condition to recover the 2D Euclidean structure (ES). Under this unified constraint, we can establish the link to other existing approaches (such as concentric circles, confocal conies) and find some novel patterns. Meanwhile, the geometric interpretation that the quadrangle formed by PAA conies is actually a rectangle with one degree of freedom is shown. Then a framework is introduced to deal with various situations of PAA conies. Finally, we propose an optimization procedure to estimate the lens distortion which is discarded by previous methods. The experiments with linear method and optimization method show the good performance of our camera calibration algorithms.